We have developed a technique called quantitative electron spectroscopic tomography (QuEST) for imaging the three-dimensional distribution of specific chemical elements in cells. A 300 kV field-emission transmission electron microscope equipped with an advanced imaging filter is used to collect a series of 2-D elemental maps for a range of specimen tilt angles. Acquisition is controlled by means of flexible computer scripts, which enable correction for specimen drift and defocus between successive tilt angles. Projected 2-D elemental distributions are obtained by acquiring images above and below characteristic core-edges in the energy-loss spectrum and by subtracting the extrapolated background intensity at each pixel. We have implemented a dual-axis simultaneous iterative reconstruction technique (SIRT) to reconstruct the 3-D elemental distribution. By applying a thickness correction algorithm that takes into account plural inelastic scattering, and by incorporating scattering cross sections for excitation of core-shell electrons, we have shown that it is possible to quantify the elemental distributions in terms of the number of atoms per voxel. Experiments are in progress to image phosphorus in three dimensions and hence to determine the density of nucleic acid in heterochromatin and euchromatin regions of the cell nucleus.